Complete the square, and solve by completing the square

Answer Key - Grade 9 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Milo solves x² - 8x = 20 by completing the square. What is the smaller solution?

   -2
2. 2.

   Noah solves x² + 6x = 16 with algebra tiles and one missing corner. What is the smaller solution?

   -8
3. 3.

   Pia solves x² - 6x = 16 (the eraser is on standby). What is the larger solution?

   8
4. 4.

   Ren's robot completes the square for x² + 12x = 64. What is the smaller solution?

   -16
5. 5.

   Tala solves x² + 8x - 9 = 0 by completing the square. What is the smaller solution?

   -9
6. 6.

   Zee plans a quilt pattern using x² - 10x - 24 = 0. What is the smaller solution?

   -2
7. 7.

   Bo's robot solves x² - 16x - 36 = 0 by completing the square. What is the larger solution?

   18
8. 8.

   Esme rewrites x² + 10x + 18 as (x + 5)² + k. What is k?

   -7
9. 9.

   Jun rewrites x² - 6x + 4 as (x - 3)² + k to find the lowest row of its table. What is k?

   -5
10. 10.

    Milo's robot rewrites x² - 14x + 40 as (x - 7)² + k. What is k?

    -9